1. King Fahd University of Petroleum & Minerals
Mechanical Engineering
Dynamics ME 201 BY
Dr. Meyassar N. Al-Haddad
Lecture # 13

2. Rectangular Coordinates

3. Normal and Tangential Coordinates

4. Cylindrical Coordinates
Resultant force components
causing a particle to move with a
known acceleration

5. Polar Coordinates Radial coordinate r Transverse coordinate q
q and r are perpendicular
Theta q in radians
1 rad = 180o/p
Direction ur and uq

6. Directions of Forces Wight force mg – vertical downward.
Normal force N – perpendicular to the tangent of path
Frictional force Ff – along the tangent in the opposite direction of motion.
Acting force Fq – along q direction Ff

7. Free-Body Diagram r q Select the object
Establish r, q coordinate system
Set ar always acts in the positive r direction
Assume aq acts in the positive q
Set W = mg always acts in a vertical direction–downward in vertical problem neglect weight in horizontal problem
Set the tangent line
Set normal force FN perpendicular to tangent line
Set frictional force Ff opposite to tangent
Set acting force F along q direction
Calculate the y angle using
Calculate other angles
Apply
tangent F ar r y FN aq Ff mg q

8. (psi) y angle Establish r = f(q) Example : r = 10t2 and q = 0.5t
r = 40q2
From geometry
(Psi) is defined between the extended radial line and the tangent to the curve.
Positive – counterclockwise sense or in the positive direction of q.
Negative – opposite direction to positive q. r 2 q q

9. Example 13-10 W = 2 Ib Smooth horizontal r = 10 t2 ft q = 0.5t rad
F = ? Tangent force at t = 1 s.

10. q r Problem m=2 kg Smooth horizontal r = 0.4 q Ptangent = ? N N=? P
At q = 45o P N r q

11. Problem 13-89
Smooth
Horizontal
m = 0.5 kg
r = (0.5 q)
q = 0.5 t2 rad
Applied force
Normal force
t = 2 s. r y y y q

12. Problem

14. Review
Example 13-11
Example 13-12

15. Thank you